As you can see (English translations are available through the links above), except for some very minor differences, these narratives are identical. Why is it that this passage is repeated in Shoftim? What is added?

The commentary of the Malbim gives a very interesting answer to this question. The story is repeated to tell about actual events (the first telling, in Yehoshua) and to give allegorical meaning to what is going on (the second telling, in Shoftim). This interpretation is based on the gemara in Temura (16a). What is the allegorical meaning?

The city of Devir (11) is also called Kiryat S’neh (Yehoshua 15:49). From this (the fact that Devir had these different names) we learn that this city was set aside as a “capital for the book” (translation of Kiryat Sefer) – that students gathered there to learn and teach from the Sefer Torah, and there was a big academy there. It was also called Kirya S’neh in connection to the verse in Devarim (33:16), which alludes to the s’neh (burning bush) where God first revealed himself to Moshe, which took place on Har Sinai, where the Torah would eventually be given. Otniel was the Rosh Yeshiva – the main teacher. As the gemara in Temura explains, 1700 of Moshe’s teachings were forgotten after he died, and Otniel was the one who was able to return them from his learning. This learning took place in his yeshiva in Devir/Kiryat Sefer/Kiryat S’neh.

When Calev challenges someone to “smite Kiray Sefer” (12) he is really asking who is able to win the battle of Torah – who is able to emerge victorious in his arguments and opinions regarding interpretations of the Torah and come to a conclusion about the halacha. In the end, Otniel is the one who was able to do this (as related in Temurah). Thus, he is the one who was able to “conquer” Kiryat Sefer – both in the real battle against the Canaanites (as related in Yehoshua) as well as in the allegorical battle (as related in Shoftom).

So Calev gives his daughter Achsa to Otniel, and she tells her father that he has given her the land of the Negev (כי ארץ הנגב נתתני) and because of this, she needs more land. The word Negev literally means dry. In Yehoshua, Achsa told her father that she was given dry, parched land, and she therefore needed something more fertile that could produce more. In Shoftim (the allegorical interpretation), she is saying that he husband has turned into an ארץ הנגב – into a “dry land” – i.e.: he is so absorbed in his Torah study that he is not tending to the physical needs of our house (he is earning a living just like a dry land), and therefore she needed some more land that would be able to provide for them (in place of what her husband would have earned).

In response to her request, Calev gives Achsa גלת עלית and גלת תחתית (the high springs and the low springs). Literally, this was land with springs that could be used to irrigate her dry land and make it more able to produce. Allegorically, Calev was telling his daughter that she already had a man who was able to bring the “water of life” (ie: Torah) from the high places (divine wisdom) and the low places (terrestrial wisdom) and that she therefore had no need for anything else, for many people would gather around her husband (see the next verse – 1:16 and the commentaries on it) and their needs would thus be taken care of.